Which of these do you want to learn more about: - What e^A means when A is a matrix - How to think about solutions to linear systems of ordinary differential equations.
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I had not seen this, I'll check it out now!
It's a really fun exercise in realizing how many ways there are to think about a mathematical object!
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Agreed. I feel like in the same spirit of the question 'how many uses can you think of for a paperclip' to measure creativity, you should always ask yourself how many ways there are to think of core ideas in a field to measure the depth of understanding.
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I feel like "linear operator" is a good one for this. I bet you could sit down and write down at least 20 different ways of thinking about, each of which adds something.
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A beautiful little result about exponentiation that should be much better known is this result of Thompson's; it says exponentiation of Hermitian matrices almost commutes.pic.twitter.com/LotR9av0cf
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Rather than framing this as something which should be better known, might it be better to say the spectral theorem and its implications should be deeper in peoples bones?
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